We report on controlled doping of an ultracold Rb gas with single neutral Cs impurity atoms. Elastic two-body collisions lead to a rapid thermalization of the impurity inside the Rb gas, representing the first realization of an ultracold gas doped with a precisely known number of impurity atoms interacting via s-wave collisions. Inelastic interactions are restricted to a single three-body recombination channel in a highly controlled and pure setting, which allows us to determine the Rb-Rb-Cs three-body loss rate with unprecedented precision. Our results pave the way for a coherently interacting hybrid system of individually controllable impurities in a quantum many-body system.

Understanding the motion of a tracer particle in a rarefied gas is of fundamental and practical importance. We report the experimental investigation of individual Cs atoms impinging on a dilute cloud of ultracold Rb atoms with variable density. We study the nonequilibrium relaxation of the initial nonthermal state and detect the effect of single collisions which has eluded observation so far. We show that after few collisions, the measured spatial distribution of the light tracer atoms is correctly described by a generalized Langevin equation with a velocity-dependent friction coefficient, over a large range of Knudsen numbers.

Di usion can be used to infer the microscopic features of a system from the observation of its macroscopic dynamics. Brownian motion accurately describes many di usive systems, but non-Brownian and nonergodic features are often observed on short timescales. Here, we trap a single ultracold caesium atom in a periodic potential and measure its di usion [1][2][3] . We engineer the particle-environment interaction to fully control motion over a broad range of di usion constants and timescales. We use a powerful stroboscopic imaging method to detect single-particle trajectories and analyse both non-equilibrium di usion properties and the approach to ergodicity 4 . Whereas the variance and two-time correlation function exhibit apparent Brownian motion at all times, higherorder correlations reveal strong non-Brownian behaviour. We additionally observe the slow convergence of the exponential displacement distribution to a Gaussian and-unexpectedly-a much slower approach to ergodicity 5 , in perfect agreement with an analytical continuous-time random-walk model [6][7][8] . Our experimental system o ers an ideal testbed for the detailed investigation of complex di usion processes.The concept of diffusion is ubiquitous in physics 9 , chemistry 10 and biology 11 . Recent developments have lead to a better understanding of the diffusive behaviour of increasingly complex structures, from colloid particles 12 and anisotropic ellipsoids 13 to extended stiff filaments 14 and fluidized matter 15 . At the same time, the diffusion of tracer particles has become a powerful experimental tool to probe the properties of complex systems from turbulent fluids 16 to living cells 17 . In many systems, diffusion is well described by the theory of Brownian motion 1 . The hallmarks of standard Brownian diffusion are: a linear mean-square displacement (MSD), σ, where D is the diffusion coefficient and · denotes the average over many trajectories; a Gaussian displacement probability distribution, a direct consequence of the central-limit theorem; and ergodic behaviour in a potential, implying that ensemble and time averages are equal in the longtime limit. Ergodicity lies at the core of statistical mechanics and indicates that a single trajectory is representative for the ensemble 4 . However, an increasing number of systems exhibit nonergodic features owing to slow, non-exponential relaxation. Examples include blinking quantum dots 18 , the motion of lipid granules 19 , and mRNA molecules 20 and receptors in living cells 21 . These systems lie outside the range of standard statistical physics and their description is hence particularly challenging 5,22 . Of special interest is the question of the approach to ergodicity. Many relevant processes in nature indeed occur on finite timescales 19-21 during which ergodic behaviour cannot be taken for granted.We experimentally realize an ideal system consisting of a single atom moving in a periodic potential and interacting with a nearresonant light field that acts as a thermal bath. Diffusion in a per...

We present an experimental system to study the Bose polaron by immersion of single, wellcontrollable neutral Cs impurities into a Rb Bose-Einstein condensate (BEC). We show that, by proper optical traps, independent control over impurity and BEC allows for precision relative positioning of the two sub-systems as well as for independent read-out. We furthermore estimate that measuring the polaron binding energy of Fröhlich-type Bose polarons in the low and intermediate coupling regime is feasible with our experimental constraints and limitations discussed.